I think one of the notable changes is regarding cross site scripting attack, and Rails 4 has guards against that kind of hacker attack built in.

In terms of MVC way of doing things, techniques, patterns, concepts, etc and Rails in general, I think your 3.2 books will still be useful. (just take note of some deprecated commands in ActiveRecord)... basically some commands have been renamed.

Heroku can host Rails4, and others too.

I started learning on 4.0 version... I figure by the time I'm really comfortable and an expert in 4.0, maybe 4.1 or 4.5 will be out. HA!

If you want to future proof your apps then it is probably better to move to Rails 4.

If you use a VPS the choice of version is up to you.

If you want to know the differences between 3 and 4 then it is best to do some research. Ryan Bates has done some tutorials at railscasts.com. The RoR wesbite also has some details and the api will give you further information.

When you do gem install rails on any system it will install the latest version. If you want to manage your Rails versions easily it might be better to use a Ruby Version Management tool such as RVM.